Something is either wrong with my wi-fi or my wireless USB adapter?

So I just got a new Comcast cable/Internet box. So the Wi-Fi is definitely working b/c my iPhone and my uncles laptop connect to it. But my Wireless USB adapter (p.s. The adapter is a Edimax 150mbps wireless 802.11b/g/n nano USB Adapter) will connect to my Wi-Fi and say its connected but the Internet won't work and i know the adapter works because it has connected to other Wi-Fi spots (that aren't mine) around it and my uncles portable Verizon Wi-Fi thing. Please help me what does this mean? Also can I just put an Ethernet cable in the back of computer and put the other end in the Comcast cable/Wi-Fi box then somehow connect them or something cause i don't know how could you tell me please. Should I just get a new wireless adapter. Also the Wi-Fi light on the cable/Wi-Fi box always flickers but the power, us/ds, and online don't they just stay still i don't know if that means anything.

This could be many things. Sometimes the firewall will block internet connections. Make sure the network is APPROVED by the firewall.

Also, you can in fact run the cable from the box to the computer. It should work right away. <-- I once hooked up the cable, got the internet working, then removed the cable, and the Wi-Fi was now working.